Semigroup C*-algebras and amenability of semigroups

Abstract

We construct reduced and full semigroup C*-algebras for left cancellative semigroups. Our new construction covers particular cases already considered by A. Nica and also Toeplitz algebras attached to rings of integers in number fields due to J. Cuntz. Moreover, we show how (left) amenability of semigroups can be expressed in terms of these semigroup C*-algebras in analogy to the group case.

39 pages; corrected and revised version, new construction added in section 3

References in corpus (1)

• C*-algebras of Toeplitz type associated with algebraic number fields

Cited by in corpus (6)

• Nuclearity of semigroup C*-algebras and the connection to amenability
• Nica-Toeplitz algebras associated with product systems over right LCM semigroups
• Inverse semigroup C*-algebras associated with left cancellative semigroups
• On the K-theory of crossed products by automorphic semigroup actions
• On K-theoretic invariants of semigroup C*-algebras attached to number fields
• An Analytic Novikov Conjecture for Semigroups